for smooth function

USAGE SUMMARY

The phrase "for smooth function" is correct and usable in written English.
It can be used when discussing the operation or performance of a system, process, or device, emphasizing the need for it to operate without issues. Example: "To ensure optimal performance, we need to implement several changes for smooth function of the software."

✓ Grammatically correct

Science

Academia

Human-verified examples from authoritative sources

Exact Expressions

2 human-written examples

It is said that the vector state X is observable algebraically, if it is expressed uniquely by X=phibigl(Y,Y^{(1)},ldots,Y^{(i }bigr), (30) for integer j and for smooth function ϕ. [33].

Advances in Difference Equations

The activity of another key enzyme, acetylcholinesterase (AChE), responsible for smooth function of nerve impulse transmission has been shown to be highly sensitive towards lead exposure in different parts of developing rat brain as well as in the erythrocytes of humans occupationally exposed to lead [ 5, 90].

BioMed Research International

Human-verified similar examples from authoritative sources

Similar Expressions

58 human-written examples

Accelerating the DC algorithm for smooth functions, Mathematical Programming 169 1, 95-118 (2019).

Stanford University

– Mixed Optimization for Smooth Functions by Mehrdad Mahdavi, Lijun Zhang and Rong Jin.

Princeton University

Here, we follow Harold Widom's seminal ideas, who proved such formulas for smooth functions decades ago.

Journal of Functional Analysis

This makes sense since for smooth functions one can 'trust' the size of the gradient to be a good indicator of how big of a step one can make (this is definitely not the case for non-smooth functions!).

Princeton University

For structured meshes, these techniques can achieve high order accuracy for smooth functions while being non-oscillatory near discontinuities.

Journal of Computational Physics

Here we present an adaptive time step memory method for smooth functions applied to the Grünwald Letnikov fractional diffusion derivative.

Journal of Computational Physics

Detection of exact fault quantity and its location is necessary for smooth functioning of a plant or industry and safety of the environment.

Journal of Loss Prevention in the Process Industries

We prove that the splines yield nearly optimal approximation order while simultaneously its piecewise derivatives provide optimal approximation of the derivatives for smooth functions.

Computer Aided Geometric Design

The grid version is evaluated by numerically intgerating the function over each bin using a non-adaptive Gauss-Kronrod scheme suited for smooth functions, falling over to a simple trapezoid scheme if this fails.

Harvard University

Expert writing Tips

Best practice

When using "for smooth function", ensure it clearly connects to a specific system, process, or component being discussed. Provide context to what exactly needs to operate smoothly.

Common error

Avoid using "for smooth function" without specifying what the function refers to. Vague usage can make the sentence unclear and less impactful. Be specific about the context.

Linguistic Context

The phrase "for smooth function" primarily serves as a prepositional phrase modifying a noun, indicating the purpose or requirement for something to operate efficiently and without issues. It describes a desired operational state.

Expression frequency: Rare

Frequent in

Science

50%

Academia

50%

News & Media

0%

Less common in

Formal & Business

0%

Encyclopedias

0%

Wiki

0%

Ludwig's WRAP-UP

The phrase "for smooth function" is a prepositional phrase indicating a requirement or purpose to achieve efficient and uninterrupted operation, commonly used in formal and scientific contexts. Ludwig AI validates its correctness and usability, although it's a relatively rare phrase. When using "for smooth function", it's crucial to specify the exact function or system you're referring to, ensuring clarity. Alternatives like "for seamless operation" or "for efficient performance" can be used depending on the context, aiming for precise and impactful communication.

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

for seamless operation

Replaces "smooth function" with "seamless operation", focusing on the uninterrupted flow.

for efficient performance

Substitutes "smooth function" with "efficient performance", highlighting effectiveness and productivity.

to ensure proper functioning

Replaces "for smooth function" with "to ensure proper functioning", shifting the focus to guaranteeing correct operation.

to facilitate optimal performance

Uses "facilitate optimal performance" instead of "smooth function", emphasizing facilitation of the best possible outcome.

for trouble-free operation

Replaces "smooth function" with "trouble-free operation", emphasizing the absence of problems.

to guarantee uninterrupted service

Changes "smooth function" to "uninterrupted service", focusing on continuity of service.

for continuous operation

Emphasizes the ongoing, uninterrupted nature of the operation.

to promote seamless workflow

Focuses on making the workflow uninterrupted and efficient.

for streamlined process

Highlights the optimization of a process to run efficiently.

for effective implementation

Emphasizes the successful and efficient execution of a plan or system.

FAQs

How can I use "for smooth function" in a sentence?

Use "for smooth function" to describe the requirements that ensure something operates effectively without issues. For example, "Regular maintenance is essential for smooth function of the machinery".

What are some alternatives to "for smooth function"?

You can use alternatives like "for seamless operation", "for efficient performance", or "to ensure proper functioning" depending on the specific context.

Is "for smooth function" formal or informal?

"For smooth function" tends to be more common in formal, technical, or scientific writing. In more casual contexts, simpler alternatives might be preferred.

What does "smooth function" mean in technical contexts?

In technical contexts, "smooth function" often refers to something operating without errors or interruptions, indicating reliability and efficiency. The phrase can also have a very specific mathematical meaning.